### Opera Optimizer Module

The Optimizer software tool can assist users in achieving optimal designs. Fully integrated with Opera, it can enable quick and easy investigations of possible design spaces for multiphysics problems. It uses an efficient optimization algorithm that combines deterministic and stochastic methods that is used to solve single and multiobjective optimization problems.

Users can set optimization problems in minutes, and leave their computer to work out the best solution for one, or multiple goals. The Optimizer saves an enormous amount of the normal design effort needed to realise a company’s design goals – whether they are lowest cost, highest performance, simplest to manufacture, smallest size (or any other parameters).

### About the module

Users can choose optimization variables from any of the user defined variables in Opera, allowing them to vary geometry data, drives and even material data in order to achieve desired objectives. By defining inequality and equality constraints users can restrict the range of the design space. They can define different levels of constraints, depending on whether they can be evaluated as a feasible design during the model creation phase or obtained as an output of the finite element analysis.

The Optimizer offers users solutions to both single objective and multiobjective problems. By defining the optimization objectives as the output of the simulation the Optimizer can then evaluate and store these. This offers users an informative set of results which they can interrogate to select the optimal design.

The Opera Optimizer uses a design of experiments method to determine the best distribution of the initial designs in the design space. Based on the mathematical model of the design space obtained using Kriging interpolation, the module deploys a stochastic method (Particle Swarm Optimization) to further advance the optimal front. The complete set of solutions is usually known as a population and each of its components (in this case the models) are known as individuals.

### Pareto-optimal solutions

In multi-objective scenarios, the algorithm identifies Pareto-optimal solutions for which no other designs have been found that are better or equivalent for all objective functions. The user can choose to store the finite element solutions of the entire population, only of the individuals that make up the Pareto front or to store the results and re-create the optimal models after the optimization is complete.

Users can define easily optimization problems using the dedicated dialogs which allow users to set:

• Design variables, along with numerical imits
• Inequality and equality constraints
• Objective functions and whether they are to be minimized or maximized

### Controlling optimization

The optimization process itself can be controlled by the user by means of:

• Termination criteria for the optimization algorithm
• Design of the initial population distribution, where the user can choose from a Standard Hammersley sequence or a regular grid
• Set of solution databases to keep

The results of the Opera optimization are displayed in the Optimization Results tab where they are dynamically updated. Optimization individuals are ranked and colour coded, with the Pareto-optimal solutions presented at the top of the list. Graphical output of the optimization data is also available, displaying the evolution of the optimization objectives (as a function of generation number), the objectives space and design space.

The user has the option of modifying optimization objectives and constraints while the optimization is running. This allows a real-time re-calibration of the optimization problem and a change in the optimization aim. In addition, optimizations can be temporarily halted and the data files moved to other disk locations or computers where the optimization can be restarted.

The Optimizer also supports a parameter sweep using a regular grid in design variable space.